Josephson Effect in Presence of Spin Berry Phase

Spin Berry phase is known to contribute to the phase coherent electronic transport in normal mecoscopic rings. Here we show that spin Berry phase can produce a persistent Josephson current as a result of the coupling between tunneling electrons and spins in the junctions. The simplest geometry where this effect is realized is a ring with three Josephson junctions with spins in each of them. Spin chirality C$_{123}$ = (S$_1$ $\times$ S$_2$) $\cdot$ S$_3$ is shown to couple to superconducting current in a way, similar to the external magnetic field coupling. Effect is shown to be a result of the interference of the Cooper pair virtual tunneling across opposite arms of the ring and is decaying exponentially with the distance with the superconducting coherence length as a natural length scale. We discuss possible realization of this effect in a multilayered magnetic-superconducting structure.